Very, very good advice.
I'm not sure I entirely agree with the last paragraph, provided the first paragraph is properly observed: if you have a history of open honesty (and mutual respect) then there are no hard barriers on behaviour in public - you will both know intuitively what is unacceptable/hurtful/undermining behaviour. Saying that, it's vital to have that well-established foundation of trust and respect before relaxing the rules.
I would add one important piece of advice though: Remember That You Will Both Screw Up. In any close relationship, you will inevitably end up hurting one another from time to time; sometimes in everyday little ways, sometimes in almighty one-off fuck-ups. Patience and forgiveness from both parties are the only medicine for such ills, and when applied liberally and sincerely, the relationship will often be stronger after the fuck-up than before.